We present accurate analytical expressions for temperatures on the upper parts of convergent plate boundaries where there are rigid plates both above and below the subduction interface. We expand on earlier formulations, which considered planar interfaces of small dip, to give expressions suitable for use on all present plate interfaces, which have both curved cross sections and maximum dips of up to 30°. We also explain the errors in studies that have asserted the inapplicability of such analytical approximations to temperatures near curved plate boundaries, or where young oceanic lithosphere is subducted. We show, by comparing these expressions with numerical solutions to the full equations, that the approximations agree with the numerical calculations to within a few percent—appreciably smaller than the uncertainties associated with the physical parameters of actual plate interfaces. The common equating of “warm” subduction interfaces with the subduction of young lithosphere, and “cold” with old lithosphere, is not valid. In the absence of dissipation, thermal gradients on the plate interface vary inversely with the product of age of the subduction ocean plate and its descent speed. Where shear stresses during slip on the plate interface exceed a ~10 MPa, the temperature gradients along the interface vary with the product of full convergence rate and shear stress during slip on the interface.

中文翻译：

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会聚板界面上的全球温度范围

我们提出了收敛板块边界上部温度的准确解析表达式，其中俯冲界面上方和下方都有刚性板块。我们扩展了早期的公式，这些公式考虑了小倾角的平面界面，以给出适用于所有现有板界面的表达式，这些板界面既有弯曲的横截面，也有高达 30° 的最大倾角。我们还解释了研究中的错误，这些研究断言这种分析近似值不适用于弯曲板块边界附近的温度，或者年轻的海洋岩石圈俯冲的地方。我们通过将这些表达式与完整方程的数值解进行比较来表明，近似值与数值计算的一致性在几个百分点之内——明显小于与实际板界面物理参数相关的不确定性。“暖”俯冲界面与年轻岩石圈的俯冲界面以及“冷”与老岩石圈的俯冲界面的常见等同是无效的。在没有耗散的情况下，板块界面上的热梯度与俯冲海洋板块的年龄及其下降速度的乘积成反比。当板界面上滑动过程中的剪切应力超过~10 MPa 时，沿界面的温度梯度随着界面上滑动过程中完全收敛速率和剪切应力的乘积而变化。而“冷”用旧岩石圈，是无效的。在没有耗散的情况下，板块界面上的热梯度与俯冲海洋板块的年龄及其下降速度的乘积成反比。当板界面上滑动过程中的剪切应力超过~10 MPa 时，沿界面的温度梯度随界面上滑动过程中完全收敛速率和剪切应力的乘积而变化。而“冷”用旧岩石圈，是无效的。在没有耗散的情况下，板块界面上的热梯度与俯冲海洋板块的年龄及其下降速度的乘积成反比。当板界面上滑动过程中的剪切应力超过~10 MPa 时，沿界面的温度梯度随界面上滑动过程中完全收敛速率和剪切应力的乘积而变化。